API / Script - Remove all selected vertices from all Vertex-Groups
Script version of @ElliotThomas answer

These two scripts have to be run in edit mode.

To remove all selected verts from all vertex groups

import bpy
context = bpy.context
ob = context.edit_object

bpy.ops.object.vertex_group_remove_from(use_all_groups=True)


Alternatively can iterate through vertex groups and use the operator on the active group.  This example does as above,  can be adjusted to skip certain groups.

import bpy
context = bpy.context
ob = context.edit_object

avg = ob.vertex_groups.active
for vg in ob.vertex_groups:
    ob.vertex_groups.active = vg
    bpy.ops.object.vertex_group_remove_from()
ob.vertex_groups.active = avg


Can also use the api method vg.remove(), for example: to remove verts with indices 0, 1 and 11 from group "Group"

C.object.vertex_groups["Group"].remove([0, 1, 11])


this has to be run in object mode, or will throw an error.